Data Sufficiency

BTGmoderatorLU wrote:Two cars are racing along two concentric circular paths. What is the ratio of the speed of the car on the outer circle to that on the inner circle, if they were to complete a lap in the same amount of time?

(1) The difference in the area between the outer circle and the inner circle is 192Ï€.
(2) The difference in radius between the outer circle and the inner circle is 8.

The OA is C.

Please, can someone assist me with this DS question? Thanks in advance!

We know that Speed = Distance/Time

Say, the speed of the car on outer circle = A, the distance traveled = x, the speed of the car on inner circle = B and the distance traveled = y

Since both the cars complete the lap in the same amount of time, we have

Ax = By (since Speed * Distance = Time)

We have to find out the value of A/B = y/x.

Let's take each statement one by one.

(1) The difference in the area between the outer circle and the inner circle is 192Ï€.

This data can help us get the value of distances. Say the radius of outer circle = R and the radius of outer circle = r

Distance traveled by car on the outer circle = 2Ï€R = x and distance traveled by car on the inner circle = 2Ï€r = y

Thus, A/B = y/x = 2Ï€r/2Ï€R = r/R

From (2), πR^2 - πr^2 = 192π

=> R^2 - r^2 = 192

We can't get the unique values of R and r; thus, r/R. Insufficient.

(2) The difference in radius between the outer circle and the inner circle is 8.

R - r = 8. We can't get the unique values of r/R. Insufficient.

(1) and (2) together

From (1), we have R^2 - r^2 = 192 => (R + r) (R - r) = 192 and from (2), we have R - r = 8, thus, R + r = 192/8 = 24

Solving R - r = 8 and R + r = 24, we R = 16 and r = 8, thus, r/R = 8/16 = 1/2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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